Ok.... my observations on the 3rd gen receiver so far...
As far as I know it must look at the header in the transmission and identify that as being a valid P38 transmission. If it detects one, then it passes it onto the BECM for decoding to make sure it is the one for your vehicle.
Just because the 3rd gen receiver stops the BECM from waking up every time there is a transmission of any kind (1st gen receiver) or a transmission on 433mhz (2nd gen with extra filtering from what I gather) it doesn't mean it's immune to interference. The only difference is, that it's now blocked at the receiver end - so if it isn't a P38 fob transmission, it won't get passed onto the BECM/cause excessive battery drain etc.
Engine Immobilised - Press Remote is not engine ECU sync. If you have lost sync then on a diesel, it will crank but not fire up and run, but you won't get any message on the dash.
Engine Immobilised is from the BECM end - as in it has immobilised the engine again. If you have the 'immobiliser' feature turned on in your BECM, then this is completely normal. The passive immobiliser will automatically immobilise the engine after it's been switched off for a period of time. The normal practice is that when you put your key back in the ignition, the key in switch tells the BECM the key is there, and it will then pulse the coil around the ignition to then get the fob to automatically send an unlock code, which the BECM will receive, and then it will allow you to start the vehicle again (it should be seamless).
If it comes up with the message on the dash, then it basically means that the BECM hasn't received a valid code from the fob automatically, which could be down to a number of things - the coil around the ignition not working or intermittent, the key in switch faulty or intermittent (so it doesn't know you've put the key back in the ignition) or maybe the 3rd gen receiver has a 'time out' function on it - where if it's inundated with interference it then goes into a time out where it waits for x long until it listens for transmissions again. Or, maybe if you've been using the caravan mover on 433, it's swamped the receiver, and it hasn't cleared the data out of whatever buffering it has, in time for it to receive the fob code from the BECM.
The easiest way to sort it... turn the passive immobiliser off in the BECM settings. This will then mean that it won't time out and immobilise the engine automatically, and it also disables the coil around the ignition (so no 'friendly sync - you'd have to do it in the door every time). The vehicle will still be immobilised when locked/alarmed - whether by the remote or the key - but when it's unlocked/disarmed it will always allow you to start it straight away.
As to why it isn't either getting the fob to automatically send a code again, or it's not receiving it - I don't know, but what it's doing by immobilising the vehicle automatically is perfectly normal with the passive immobiliser switched on.
'06 4.2 Supercharged Black/Cream "Jess" -- Bought April 2021 (NZ)
'01 4.6 Vogue Black/Lightstone "Snog" -- Bought Jan 2012
'99 4.6 HSE Cobar Blue/Lightstone -- Sold March 2009
'95 4.6 HSE Epsom Green/Tan -- Traded June 2008